Quadratic Equations and Inequalities

2.1

Quadratic Equations and Inequalities

Definition of Quadratic Equation

A quadratic equation in general form can be wirtten as
$ax^2+bx+c=0$
where

$a$, $b$ and $c$ are constants and $a \neq0$.

$The image is an educational graphic titled ‘Methods of Solving Quadratic Equations.’ It features two methods: 1. ‘Completing the Square Method’: - Rewrite $ ax^2 + bx + c = 0 $ in the form of $ a(x - h)^2 + k = 0 $. - Solve for $ x $. 2. ‘Formula Method’: - Use the formula $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $. The graphic includes the Pandai logo at the bottom right corner.$

Quadratic Equation Properties

If $\alpha$ and $\beta$ are the roots of a quadratic equation, then
$(x-\alpha)(x-\beta)=0$
or
$x^2-(\alpha+\beta)x+\alpha\beta=0$
For $x^2-(\alpha+\beta)x+\alpha\beta=0$,
$\alpha+\beta$ is the sum of roots and $\alpha\beta$ is the product of roots.
For a quadratic equation in the form $(x-a)(x-b)=0$, where $a \lt b$,
if $(x-a)(x-b)\gt0$, then $x \lt a$ or $x \gt b$.
if $(x-a)(x-b)\lt0$, then $a\lt x \lt b$.